Mathematical and statistical modeling techniques are relevant to biomedical investigations at a variety of scales and in a variety of contexts. Our Lab applies expertise in the mathematical, statistical and computing sciences to address novel problems arising in cutting edge areas of biomedical research.[unreadable] [unreadable] In a joint study with investigators in Laboratory of Molecular Biology, NCI and Institut National de la Recherche Agronomique (INRA), France, we are attacking the problem of protein structure classification, with the goal of improving automated methods for recognition and classification of protein domains in three dimensional structures. Domains are thought to be the building blocks of complex structures, and often determine protein function. We have recently shown that two distinct structure similarity measures (VAST and SHEBA) can obtain at best about 75-80% agreement with a standard manually curated protein classification (SCOP), calling into question the existence of sharp boundaries between protein "folds". Currently, we are exploring hierarchical cluster analysis as a means of improving that agreement. A comparison of pairwise similarity measures with expert opinion showed that excellent agreement, yet classes defined by pairwise similarity differed significantly from generally accepted "fold" definitions.[unreadable] [unreadable] With an investigator in the Laboratory of Receptor Biology and Gene Expression, National Cancer Institute, and with another investigator from Imperial College, London, we have studied the physical topology of gene and chromosome placement in cell nuclei. This work requires careful statistical analysis on gene and chromosome placement data. We have shown that in mice, the gene MASH1, involved in early embryonic neurogenesis, is preferentially placed in the nuclear periphery in embryonic stem cells, but migrates towards the nuclear center after commitment to neural development. It was also shown that the physical change in location was coupled to changes in expression level and to changes in chromatin structure along a 2MB region of the genome centered about the MASH1 locus.[unreadable] [unreadable] With an investigator from the Laboratory of Receptor Biology and Gene Expression, National Cancer Institute, we continued our studies of the spatial organization of the genome. In 2006 we showed that in mouse cells, spatial correlations between chromosomes is not merely due to their radial placement. We are now investigating the effects of gene splicing on genetic disease, with particular emphasize on high through-put analysis of cell batches, which will be useful in finding drug targets.[unreadable] [unreadable] With an investigator in the Division of International Epidemiology, Fogarty International Center, we have developed a phenomenological model of Plasmodium parasite/red blood cell dynamics, and have used it to examine the consequences of strategies of attack of the different Plasmodium species that attack humans. Currently, we are investigating consequences of dual P. vivax- P. falciparum infection. (PCR studies indicate that about 10% of all human malaria cases are dual P. vivax-P. falciparum infections.) Our studies indicate transients in red blood cell production induced in response to P. falciparum invasion of such cells can greatly boost the parasitemia of P. vivax, even inducing a cryptic infection into a more dangerous phase.[unreadable] [unreadable] In a project with investigators of NIMH, we analyzed multiple-electrode recordings from in-vitro neural network preparations in order to deduce the underlying cortical network topology. We found that such functional networks show a strong "small world" property, meaning high clustering among the nodes and short node-to-node distances. More importantly, we found a novel property of these networks when the weights of the network links are taken into account. Simulations indicate that such network architecture can be obtained using special, time-delayed learning rules.[unreadable] [unreadable] In a continuing project with investigators in the Laboratory of Integrative and Medical Biophysics, NICHD related to the development of diffusion tensor MRI, we developed methods for spectral decomposition of a 4th-order covariance tensor and showed how it can be applied to diffusion tensor MRI.